How do i prove the following using the properties of absolute values?
A) |x|^2 = x^2
B) |x| = sqrt{ x^2}
Thanks
For both you can use the fact that:
$\displaystyle |x| = \left \{ \begin{array}{cc}x, &\mbox { if } x \geq 0\\-x, &\mbox { if } x < 0 \end{array}\right.$
and show that the functions on the right satisfy the same function. Part B is actually an alternative definition for |x|